Equivalent Expressions - Examples, Exercises and Solutions

In previous articles, we have talked about what an algebraic expression is and how to get the numerical value of algebraic expressions. Today, we will cover equivalent expressions.

Equivalent expressions are two or more algebraic expressions that represent the same value. They may have a different structure, but their numerical value will be the same.

For example, in the following equation both sides represent the same quantity:

$9X=3X+6X$

Below is another example with 2 variables. By simplifying the expressions on both sides of the equation, we can work out that on both we have $2X-3Y+5$ and therefore the expressions are equivalent.

$2X-3Y+5=X+X-2Y+10-5-Y$

Practice Equivalent Expressions

Question 1

$18x-7+4x-9-8x=\text{?}$

Question 2

$7.3\cdot4a+2.3+8a=\text{?}$

Question 3

$\frac{9m}{3m^2}\times\frac{3m}{6}=$

Question 4

Are the expressions the same or not?

$$ 18x $$

$$ 2+9x $$

Question 5

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

Examples with solutions for Equivalent Expressions

Exercise #1

$18x-7+4x-9-8x=\text{?}$

Video Solution

Step-by-Step Solution

To solve the exercise, we will reorder the numbers using the substitution property.

$18x-8x+4x-7-9=$

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

$18x-8x=10x$ $10x+4x=14x$ $-7-9=-16$ Remember, these two numbers cannot be added or subtracted, so the result is:

$14x-16$

Answer

$14x-16$

Exercise #2

$7.3\cdot4a+2.3+8a=\text{?}$

Video Solution

Step-by-Step Solution

It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.

We group the elements:

$7.3×4a + 2.3 + 8a =$

$29.2a + 2.3 + 8a =$

$37.2a + 2.3$

And in this exercise, this is the solution!

You can continue looking for the value of a.

But in this case, there is no need.

Answer

$37.2a+2.3$

Exercise #3

$\frac{9m}{3m^2}\times\frac{3m}{6}=$

Video Solution

Step-by-Step Solution

According to the laws of multiplication, we must first simplify everything into one exercise:

$\frac{9m\times3m}{3m^2\times6}=$

We will simplify and get:

$\frac{9m^2}{m^2\times6}=$

We will simplify and get:

$\frac{9}{6}=$

We will factor the expression into a multiplication:

$\frac{3\times3}{3\times2}=$

We will simplify and get:

$\frac{3}{2}=1.5$

Answer

$0.5m$

Exercise #4

Are the expressions the same or not?

$18x$

$2+9x$

Video Solution

Answer

Exercise #5

Are the expressions the same or not?

$20x$

$2\times10x$

Video Solution

Answer

Yes

Question 1

Are the expressions the same or not?

$$ 3+3+3+3 $$

$3\times4$

Question 2

$$ 11+5x-2x+8= $$

Question 3

$3x+4x+7+2=\text{?}$

Question 4

$3z+19z-4z=\text{?}$

Question 5

$$ 5+0+8x-5= $$

Answer

$8X$

Question 1

$$ 5+8-9+5x-4x= $$

Question 2

$$ x+x= $$

Question 3

Are the expressions the same or not?

$0.5x\times1$

$$ 0.5x+0 $$

Question 4

Are the expressions the same or not?

$$ 15x-30 $$

$$ 45-15-5x+15x $$

Question 5

$$ 35m+9n-48m+52n=? $$

Exercise #11

$5+8-9+5x-4x=$

Video Solution

Answer

4+X

Exercise #12

$x+x=$

Video Solution

Answer

$2x$

Exercise #13

Are the expressions the same or not?

$0.5x\times1$

$0.5x+0$

Video Solution

Answer

Yes

Exercise #14

Are the expressions the same or not?

$15x-30$

$45-15-5x+15x$

Video Solution

Answer

Exercise #15

$35m+9n-48m+52n=?$

Video Solution

Answer

$61n-13m$

Topics learned in later sections